Abstract
This paper studies Newtonian Sobolev-Lorentz spaces. We prove that these spaces are Banach. We also study the global p, q-capacity and the p, q-modulus of families of rectifiable curves. Under some additional assumptions (that is, X carries a doubling measure and a weak Poincare inequality), we show that when 1 ≤ q 1. We provide a counterexample for the density result in the Euclidean setting when 1 < p ≤ n and q =∞.
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